The spatial distribution of clusters and the formation of mixed languages in bilingual competition

We use cellular automata simulation methods to study the competition between two languages (language A$A$ and B$B$). We assume each of the two languages consists of F$F$ independent features and define an individual as two F$F$-length “identity level” integer strings. The value of each integer of the strings indicates whether the individual is willing or unwilling to express a certain feature and how his willingness or unwillingness is. In our model, individuals who speak either language A$A$ or B$B$ are randomly placed on a square lattice initially and programmed to evolve under the communication and interaction methods. First, we consider the situation that the competition occurs between two languages with only one feature. We find the differences between short-time coexistence processes and long-time coexistence processes and discuss how the spatial distribution of languages evolves. We observe that periodic line-shaped boundaries take shape in some simulations and lead to long-time coexistence between the two languages. Then we study the multi-feature cases when F=10$F=10$ and find the correlation among the evolution of different features decreases with time. We also observe the extinction of two primitive languages and formation of mixed languages.     

Two charges on a plane in a magnetic field: II. Moving neutral quantum system across a magnetic field

The moving neutral system of two Coulomb charges on a plane subject to a constant magnetic field B$B$ perpendicular to the plane is considered. It is shown that the composite system of finite total mass is bound for any center-of-mass momentum P$P$ and magnetic field strength; the energy of the ground state is calculated accurately using a variational approach. Its accuracy is cross-checked in a Lagrange-mesh method for B=1$B=1$  a.u. and in a perturbation theory at small B$B$ and P$P$. The constructed trial function has the property of being a uniform approximation of the exact eigenfunction. For a Hydrogen atom and a Positronium a double perturbation theory in B$B$ and P$P$ is developed and the first corrections are found algebraically. A phenomenon of a sharp change of energy behavior for a certain center-of-mass momentum and a fixed magnetic field is indicated.     

Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach

A generalization of the pure site and pure bond percolation problems called site–bond percolation on a triangular lattice is studied. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S∩B$S\cap B$ and S∪B$S\cup B$) for site–bond percolation are used. In S∩B$S\cap B$ (S∪B$S\cup B$), two points are said to be connected if a sequence of occupied sites and (or  ) bonds joins them. By using finite-size scaling theory, data from S∩B$S\cap B$ and S∪B$S\cup B$ are analyzed in order to determine (i$i$) the phase boundary between the percolating and non-percolating regions and (ii$ii$) the numerical values of the critical exponents of the phase transition occurring in the system. A theoretical approach, based on exact calculations of configurations on finite triangular cells, is applied to study the site–bond percolation on triangular lattices. The percolation processes have been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied elements. A comparison of the results obtained by these two methods has been performed and discussed.     

Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

The maximum entropy (MaxEnt) principle is a versatile tool for statistical inference of the probability density function (pdf) from its moments as a least-biased estimation among all other possible pdf’s. It maximizes Shannon entropy, satisfying the moment constraints. Thus, the MaxEnt algorithm transforms the original constrained optimization problem to the unconstrained dual optimization problem using Lagrangian multipliers. The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments (m>5–10)$(m>5''–''10)$ due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities. Classic MaxEnt algorithms overcome these difficulties by using orthogonal polynomials, which enable roughly the same sensitivity for all Lagrangian multipliers. In this paper, we employ an idea based on different principles, using Fup_n${\mathit{Fup}}_n$ basis functions with compact support, which can exactly describe algebraic polynomials, but only if the Fup order-n   is greater than or equal to the polynomial’s order. Our algorithm solves the CMP with respect to the moments of only low order Fup₂${\mathit{Fup}}_2$ basis functions, finding a Fup₂${\mathit{Fup}}_2$ optimal pdf with better balanced Lagrangian multipliers. The algorithm is numerically very efficient due to localized properties of Fup₂${\mathit{Fup}}_2$ basis functions implying a weaker dependence between Lagrangian multipliers and faster convergence. Only consequences are an iterative scheme of the algorithm where power moments are a sum of Fup₂${\mathit{Fup}}_2$ and residual moments and an inexact entropy upper bound. However, due to small residual moments, the algorithm converges very quickly as demonstrated on two continuous pdf examples – the beta distribution and a bi-modal pdf, and two discontinuous pdf examples – the step and double Dirac pdf. Finally, these pdf examples present that Fup MaxEnt algorithm yields smaller entropy value than classic MaxEnt algorithm, but differences are very small for all practical engineering purposes.     

Dirac oscillator in perpendicular magnetic and transverse electric fields

We study (2+1)$(2+1)$ dimensional massless Dirac oscillator in the presence of perpendicular magnetic and transverse electric fields. Exact solutions are obtained and it is shown that there exists a critical magnetic field B_c$B_c$ such that the spectrum is different in the two regions B>B_c$B>B_c$ and B<B_c$B<B_c$. The situation is also analyzed for the case B=B_c$B=B_c$.     

The phase diagram of a ferrimagnetic multilayer system with disordered interface layers

The critical and compensation behaviors of a ferrimagnetic multilayer system on a simple cubic structure consisting of L layer of spin-1/2 A atoms, L   layers of spin-1 B atoms and a disordered interface with two layers in between that is characterized by a random arrangement of A and B atoms of _APB1-P${\mathrm{A}}_P{\mathrm{B}}_{1-P}$ type in the first layer and _A1-PBP${\mathrm{A}}_{1-P}{\mathrm{B}}_P$ type in the second layer and a negative A–B coupling, are examined using the effective field theory based on a probability distribution technique. The effect of the probability p$p$, interactions, different anisotropy and the thickness L on the magnetic properties is examined. The obtained results show a number of characteristic features, such as the possibility of many compensation points.     

Probing photon helicity in radiative B decays via charmonium resonance interference

We investigate a new method to probe the helicity of the photon emitted in the b→sγ$b\to s\gamma$ transition. The method relies on the observation of interference effects between two resonance contributions, B→K^∗(Kγ)γ$B\to K^{\ast }(K\gamma )\gamma$ and B→ηc(γγ)K$B\to {\eta }_c(\gamma \gamma )K$ or B→χ_c0(γγ)K$B\to {\chi }_{c0}(\gamma \gamma )K$ to the same final state Kγγ  . Decays of the type B→Kres(Kγ)γ$B\to K_{\mathrm{res}}(K\gamma )\gamma$ dominate the B→Kγγ$B\to K\gamma \gamma$ yield throughout most of the phase space, and may be accessible at current B meson facilities already.     

Euler–Heisenberg effective action and magnetoelectric effect in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field B$B$ (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field E$E$ at E/B?1$E/B?1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field E$E$ and the lowest order correction to it due to the magnetic field (B/E?1$B/E?1$).     

Third-harmonic generation in asymmetric coupled quantum wells

The third-harmonic generation (THG) in asymmetric coupled quantum wells (ACQWs) for different values of the well parameter Δ$\Delta$ and width of barrier (_WB)$\left(W_B\right)$ are theoretically studied. The analytical expression of the third-harmonic generation is derived by using the compact density-matrix approach and the iterative method. Finally, the numerical calculations are presented for typical GaAs/Al_xGa_1−xAs asymmetric coupled quantum wells. Results obtained show that the third-harmonic generation in the asymmetric coupled quantum wells can be importantly modified by the parameter Δ$\Delta$ and _WB$W_B$. Moreover, third-harmonic generation also depends on the relaxation rate of the asymmetric coupled quantum wells.     

Nonextensivity measure for earthquake networks

Studying earthquakes and the associated geodynamic processes based on the complex network theory enables us to learn about the universal features of the earthquake phenomenon. In addition, we can determine new indices for identification of regions geophysically. It was found that earthquake networks are scale free and its degree distribution obeys the power law. Here we claim that the q$q$-exponential function is better than power law model for fitting the degree distribution. We also study the behavior of q$q$ parameter (nonextensivity measure) with respect to resolution. It was previously asserted in Eur. Phys. J. B (2012) 85: 23; that the topological characteristics of earthquake networks are dependent on each other for large values of the resolution. A peak in the plot of q$q$ against resolution determines the beginning of the assertion range.     

Suppression of flavor symmetry breaking in B decay sum rules

While flavor symmetries are useful for studying hadronic B   decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B→Kπ$B\to K\pi$ decays, where isospin breaking is shown to be negligible. (2) An SU(3)$\mathrm{SU}(3)$ sum rule for pairs of B→Kπ$B\to K\pi$ and B→Kη₈$B\to K{\eta }_8$, generalized to pairs of B→Kπ$B\to K\pi$, B→Kη$B\to K\eta$ and B→Kη^′$B\to K{\eta }^{\prime }$.     

New method to constrain the relativistic free-streaming gas in the Universe

We discuss a method to constrain the fraction density f of the relativistic gas in the radiation-dominant stage, by their impacts on a relic gravitational waves and the cosmic microwave background (CMB) B-polarization power spectrum. We find that the uncertainty of f   strongly depends on the noise power spectra of the CMB experiments and the amplitude of the gravitational waves. Taking into account of the CMBPol instrumental noises, an uncertainty Δf=0.046$\mathrm{\Delta }f=0.046$ is obtained for the model with tensor-to-scalar ratio r=0.1$r=0.1$. For an ideal experiment with only the reduced cosmic lensing as the contamination of B  -polarization, Δf=0.008$\mathrm{\Delta }f=0.008$ is obtained for the model with r=0.1$r=0.1$. So the precise observation of the CMB B-polarization provides a great opportunity to study the relativistic components in the early Universe.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

Naturally light sterile neutrinos from theory of R-parity

The fate of R-parity is one of the central issues in the minimal supersymmetric standard model (MSSM). Gauged B−L$B-L$ symmetry provides a natural framework for addressing this question. Recently, it was pointed out that the minimal such theory does not need any additional Higgs if the B−L$B-L$ breaking is achieved through the VEVs of right-handed sneutrinos, which ties the new physics scale to the scale of the MSSM. We show here that this immediately leads to an important prediction of two light sterile neutrinos, which can play a significant role in the BBN and neutrino oscillations. We also discuss some new relevant phenomenology for the LHC, in the context of the minimal supersymmetric left–right symmetric theory which provides a natural setting for the gauged B−L$B-L$ symmetry.